A note on a nonlinear eigenvalue problem |
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Authors: | Giovanna Cerami |
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Institution: | (1) Present address: Dipartimento di Matematica, Università della Calabria, 87036 Arcavacata di Rende (Cosenza), Italy |
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Abstract: | Summary In this paper a necessary and sufficient condition for the existence of negative eigenvalues for the problem- u – u=![mgr](/content/u3q4414q0738rx73/xxlarge956.gif) (x)¦u¦p–2u in u¦![part](/content/u3q4414q0738rx73/xxlarge8706.gif) =0 is given. Here Rn is supposed a smooth bounded domain, 0 a bounded nonnegative function, ( 1, 2), 1 and 1 being the first and the second eigenvalue of - in with zero Dirichlet boundary data, p 2 and, if n 3, p < 2n¦(n–2). Moreover in the linear case (p=2) a uniqueness result is proved.Work supported by G.N.A.F.A. and by M.P.I, of Italy Fondi 40% Equazioni Differenziali e Calcolo delle Variazioni and Fondi 60% Analisi matematica. |
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